Package Modelica.Electrical.Machines.BasicMachines.SynchronousInductionMachinesModels of synchronous induction machines
Package Modelica.Electrical.Machines.BasicMachines.SynchronousInductionMachinesThis package contains models of synchronous induction machines, based on space phasor theory:
Extends from Modelica.Icons.VariantsPackage (Icon for package containing variants).
| Name | Description |
|---|---|
SM_ElectricalExcited | Electrical excited synchronous induction machine with damper cage |
SM_PermanentMagnet | Permanent magnet synchronous induction machine |
SM_ReluctanceRotor | Synchronous induction machine with reluctance rotor and damper cage |
Model Modelica.Electrical.Machines.BasicMachines.SynchronousInductionMachines.SM_PermanentMagnet
Model of a three phase permanent magnet synchronous induction machine.
Resistance and stray inductance of stator is modeled directly in stator phases, then using space phasor transformation and a rotor-fixed AirGap model. Resistance and stray inductance of rotor's squirrel cage is modeled in two axis of the rotor-fixed coordinate system. Permanent magnet excitation is modelled by a constant equivalent excitation current feeding the d-axis. The machine models take the following loss effects into account:
Whether a damper cage is present or not, can be selected with Boolean parameter useDamperCage (default = true).
Default values for machine's parameters (a realistic example) are:
| number of pole pairs p | 2 | |
| stator's moment of inertia | 0.29 | kg.m2 |
| rotor's moment of inertia | 0.29 | kg.m2 |
| nominal frequency fNominal | 50 | Hz |
| nominal voltage per phase | 100 | V RMS |
| no-load voltage per phase | 112.3 | V RMS @ nominal speed |
| nominal current per phase | 100 | A RMS |
| nominal torque | 181.4 | Nm |
| nominal speed | 1500 | rpm |
| nominal mechanical output | 28.5 | kW |
| nominal rotor angle | 20.75 | degree |
| efficiency | 95.0 | % |
| power factor | 0.98 | |
| stator resistance | 0.03 | Ohm per phase at reference temperature |
| reference temperature TsRef | 20 | °C |
| temperature coefficient alpha20s | 0 | 1/K |
| stator reactance Xd | 0.4 | Ohm per phase in d-axis |
| stator reactance Xq | 0.4 | Ohm per phase in q-axis |
| stator stray reactance Xss | 0.1 | Ohm per phase |
| damper resistance in d-axis | 0.04 | Ohm at reference temperature |
| damper resistance in q-axis | same as d-axis | |
| reference temperature TrRef | 20 | °C |
| temperature coefficient alpha20r | 0 | 1/K |
| damper stray reactance in d-axis XDds | 0.05 | Ohm |
| damper stray reactance in q-axis XDqs | same as d-axis | |
| stator operational temperature TsOperational | 20 | °C |
| damper operational temperature TrOperational | 20 | °C |
| These values give the following inductances: | ||
| main field inductance in d-axis | (Xd - Xss)/(2*pi*fNominal) | |
| main field inductance in q-axis | (Xq - Xss)/(2*pi*fNominal) | |
| stator stray inductance per phase | Xss/(2*pi*fNominal) | |
| damper stray inductance in d-axis | XDds/(2*pi*fNominal) | |
| damper stray inductance in q-axis | XDqs/(2*pi*fNominal) |
Extends from Modelica.Electrical.Machines.Interfaces.PartialBasicInductionMachine (Partial model for induction machine).
| Type | Name | Default | Description |
|---|---|---|---|
final Integer | m | 3 | Number of phases |
Integer | p | Number of pole pairs (Integer) | |
Frequency | fsNominal | Nominal frequency | |
Temperature | TsOperational | Operational temperature of stator resistance | |
Resistance | Rs | Stator resistance per phase at TRef | |
Temperature | TsRef | Reference temperature of stator resistance | |
LinearTemperatureCoefficient20 | alpha20s | Temperature coefficient of stator resistance at 20 degC | |
Inductance | Lszero | Lssigma | Stator zero sequence inductance |
Inductance | Lssigma | Stator stray inductance per phase | |
Inertia | Jr | Rotor's moment of inertia | |
Boolean | useSupport | false | Enable / disable (=fixed stator) support |
Inertia | Js | Jr | Stator's moment of inertia |
Boolean | useThermalPort | false | Enable / disable (=fixed temperatures) thermal port |
FrictionParameters | frictionParameters | Friction loss parameter record | |
CoreParameters | statorCoreParameters | Stator core loss parameter record; all parameters refer to stator side | |
StrayLoadParameters | strayLoadParameters | Stray load loss parameter record | |
final Temperature | TpmOperational | 293.15 | Operational temperature of permanent magnet |
Temperature | TrOperational | Operational temperature of (optional) damper cage | |
Voltage | VsOpenCircuit | Open circuit RMS voltage per phase @ fsNominal | |
Inductance | Lmd | Stator main field inductance per phase in d-axis | |
Inductance | Lmq | Stator main field inductance per phase in q-axis | |
Boolean | useDamperCage | Enable / disable damper cage | |
Inductance | Lrsigmad | Damper stray inductance in d-axis | |
Inductance | Lrsigmaq | Lrsigmad | Damper stray inductance in q-axis |
Resistance | Rrd | Damper resistance in d-axis at TRef | |
Resistance | Rrq | Rrd | Damper resistance in q-axis at TRef |
Temperature | TrRef | Reference temperature of damper resistances in d- and q-axis | |
LinearTemperatureCoefficient20 | alpha20r | Temperature coefficient of damper resistances in d- and q-axis | |
PermanentMagnetLossParameters | permanentMagnetLossParameters | Permanent magnet loss parameter record |
| Type | Name | Description |
|---|---|---|
Flange_a | flange | Shaft |
Flange_a | support | Support at which the reaction torque is acting |
PositivePlug | plug_sp | Positive stator plug |
NegativePlug | plug_sn | Negative stator plug |
ThermalPortSMPM | thermalPort | |
output RealOutput | ir[2] | Damper cage currents |
output RealOutput | idq_dr[2] | Damper space phasor current / rotor fixed frame |
Model Modelica.Electrical.Machines.BasicMachines.SynchronousInductionMachines.SM_ElectricalExcited
Model of a three phase electrical excited synchronous induction machine with damper cage.
Resistance and stray inductance of stator is modeled directly in stator phases, then using space phasor transformation and a rotor-fixed AirGap model. Resistance and stray inductance of rotor's squirrel cage is modeled in two axis of the rotor-fixed coordinate system. Electrical excitation is modelled by converting excitation current and voltage to d-axis space phasors. The machine models take the following loss effects into account:
Whether a damper cage is present or not, can be selected with Boolean parameter useDamperCage (default = true).
Default values for machine's parameters (a realistic example) are:
| number of pole pairs p | 2 | |
| stator's moment of inertia | 0.29 | kg.m2 |
| rotor's moment of inertia | 0.29 | kg.m2 |
| nominal frequency fNominal | 50 | Hz |
| nominal voltage per phase | 100 | V RMS |
| no-load excitation current @ nominal voltage and frequency |
10 | A DC |
| warm excitation resistance | 2.5 | Ohm |
| nominal current per phase | 100 | A RMS |
| nominal apparent power | -30000 | VA |
| power factor | -1.0 | ind./cap. |
| nominal excitation current | 19 | A |
| efficiency w/o excitation | 97.1 | % |
| nominal torque | -196.7 | Nm |
| nominal speed | 1500 | rpm |
| nominal rotor angle | -57.23 | degree |
| stator resistance | 0.03 | Ohm per phase at reference temperature |
| reference temperature TsRef | 20 | °C |
| temperature coefficient alpha20s | 0 | 1/K |
| stator reactance Xd | 1.6 | Ohm per phase in d-axis |
| giving Kc | 0.625 | |
| stator reactance Xq | 1.6 | Ohm per phase in q-axis |
| stator stray reactance Xss | 0.1 | Ohm per phase |
| damper resistance in d-axis | 0.04 | Ohm at reference temperature |
| damper resistance in q-axis | same as d-axis | |
| reference temperature TrRef | 20 | °C |
| temperature coefficient alpha20r | 0 | 1/K |
| damper stray reactance in d-axis XDds | 0.05 | Ohm |
| damper stray reactance in q-axis XDqs | same as d-axis | |
| excitation resistance | 2.5 | Ohm at reference temperature |
| reference temperature TeRef | 20 | °C |
| temperature coefficient alpha20e | 0 | 1/K |
| excitation stray inductance | 2.5 | % of total excitation inductance |
| stator operational temperature TsOperational | 20 | °C |
| damper operational temperature TrOperational | 20 | °C |
| excitation operational temperature TeOperational | 20 | °C |
| These values give the following inductances: | ||
| main field inductance in d-axis | (Xd - Xss)/(2*pi*fNominal) | |
| main field inductance in q-axis | (Xq - Xss)/(2*pi*fNominal) | |
| stator stray inductance per phase | Xss/(2*pi*fNominal) | |
| damper stray inductance in d-axis | XDds/(2*pi*fNominal) | |
| damper stray inductance in q-axis | XDqs/(2*pi*fNominal) |
Extends from Modelica.Electrical.Machines.Interfaces.PartialBasicInductionMachine (Partial model for induction machine).
| Type | Name | Default | Description |
|---|---|---|---|
final Integer | m | 3 | Number of phases |
Integer | p | Number of pole pairs (Integer) | |
Frequency | fsNominal | Nominal frequency | |
Temperature | TsOperational | Operational temperature of stator resistance | |
Resistance | Rs | Stator resistance per phase at TRef | |
Temperature | TsRef | Reference temperature of stator resistance | |
LinearTemperatureCoefficient20 | alpha20s | Temperature coefficient of stator resistance at 20 degC | |
Inductance | Lszero | Lssigma | Stator zero sequence inductance |
Inductance | Lssigma | Stator stray inductance per phase | |
Inertia | Jr | Rotor's moment of inertia | |
Boolean | useSupport | false | Enable / disable (=fixed stator) support |
Inertia | Js | Jr | Stator's moment of inertia |
Boolean | useThermalPort | false | Enable / disable (=fixed temperatures) thermal port |
FrictionParameters | frictionParameters | Friction loss parameter record | |
CoreParameters | statorCoreParameters | Stator core loss parameter record; all parameters refer to stator side | |
StrayLoadParameters | strayLoadParameters | Stray load loss parameter record | |
Temperature | TrOperational | Operational temperature of (optional) damper cage | |
Inductance | Lmd | Stator main field inductance per phase in d-axis | |
Inductance | Lmq | Stator main field inductance per phase in q-axis | |
Boolean | useDamperCage | Enable / disable damper cage | |
Inductance | Lrsigmad | Damper stray inductance in d-axis | |
Inductance | Lrsigmaq | Lrsigmad | Damper stray inductance in q-axis |
Resistance | Rrd | Damper resistance in d-axis at TRef | |
Resistance | Rrq | Rrd | Damper resistance in q-axis at TRef |
Temperature | TrRef | Reference temperature of damper resistances in d- and q-axis | |
LinearTemperatureCoefficient20 | alpha20r | Temperature coefficient of damper resistances in d- and q-axis | |
Voltage | VsNominal | Nominal stator RMS voltage per phase | |
Current | IeOpenCircuit | Open circuit excitation current @ nominal voltage and frequency | |
Resistance | Re | Excitation resistance at TRef | |
Temperature | TeRef | Reference temperature of excitation resistance | |
LinearTemperatureCoefficient20 | alpha20e | Temperature coefficient of excitation resistance | |
Real | sigmae | Stray fraction of total excitation inductance | |
Temperature | TeOperational | Operational excitation temperature | |
BrushParameters | brushParameters | Brush loss parameter record |
| Type | Name | Description |
|---|---|---|
Flange_a | flange | Shaft |
Flange_a | support | Support at which the reaction torque is acting |
PositivePlug | plug_sp | Positive stator plug |
NegativePlug | plug_sn | Negative stator plug |
ThermalPortSMEE | thermalPort | |
output RealOutput | ir[2] | Damper cage currents |
output RealOutput | idq_dr[2] | Damper space phasor current / rotor fixed frame |
PositivePin | pin_ep | Positive excitation pin |
NegativePin | pin_en | Negative excitation pin |
Model Modelica.Electrical.Machines.BasicMachines.SynchronousInductionMachines.SM_ReluctanceRotor
Model of a three phase synchronous induction machine with reluctance rotor and damper cage.
Resistance and stray inductance of stator is modeled directly in stator phases, then using space phasor transformation. Resistance and stray inductance of rotor's squirrel cage is modeled in two axis of the rotor-fixed coordinate system. Both together connected via a rotor-fixed AirGap model. The machine models take the following loss effects into account:
Whether a damper cage is present or not, can be selected with Boolean parameter useDamperCage (default = true).
Default values for machine's parameters (a realistic example) are:
| number of pole pairs p | 2 | |
| stator's moment of inertia | 0.29 | kg.m2 |
| rotor's moment of inertia | 0.29 | kg.m2 |
| nominal frequency fNominal | 50 | Hz |
| nominal voltage per phase | 100 | V RMS |
| nominal current per phase | 50 | A RMS |
| nominal torque | 46 | Nm |
| nominal speed | 1500 | rpm |
| nominal mechanical output | 7.23 | kW |
| efficiency | 96.98 | % |
| power factor | 0.497 | |
| stator resistance | 0.03 | Ohm per phase at reference temperature |
| reference temperature TsRef | 20 | °C |
| temperature coefficient alpha20s | 0 | 1/K |
| rotor resistance in d-axis | 0.04 | Ohm at reference temperature |
| rotor resistance in q-axis | same as d-axis | |
| reference temperature TrRef | 20 | °C |
| temperature coefficient alpha20r | 0 | 1/K |
| stator reactance Xsd in d-axis | 3 | Ohm per phase |
| stator reactance Xsq in q-axis | 1 | Ohm |
| stator stray reactance Xss | 0.1 | Ohm per phase |
| rotor stray reactance in d-axis Xrds | 0.05 | Ohm per phase |
| rotor stray reactance in q-axis Xrqs | same as d-axis | |
| stator operational temperature TsOperational | 20 | °C |
| damper operational temperature TrOperational | 20 | °C |
| These values give the following inductances: | ||
| stator stray inductance per phase | Xss/(2*pi*fNominal) | |
| rotor stray inductance in d-axis | Xrds/(2*pi*fNominal) | |
| rotor stray inductance in q-axis | Xrqs/(2*pi*fNominal) | |
| main field inductance per phase in d-axis | (Xsd-Xss)/(2*pi*fNominal) | |
| main field inductance per phase in q-axis | (Xsq-Xss)/(2*pi*fNominal) |
Extends from Modelica.Electrical.Machines.Interfaces.PartialBasicInductionMachine (Partial model for induction machine).
| Type | Name | Default | Description |
|---|---|---|---|
final Integer | m | 3 | Number of phases |
Integer | p | Number of pole pairs (Integer) | |
Frequency | fsNominal | Nominal frequency | |
Temperature | TsOperational | Operational temperature of stator resistance | |
Resistance | Rs | Stator resistance per phase at TRef | |
Temperature | TsRef | Reference temperature of stator resistance | |
LinearTemperatureCoefficient20 | alpha20s | Temperature coefficient of stator resistance at 20 degC | |
Inductance | Lszero | Lssigma | Stator zero sequence inductance |
Inductance | Lssigma | Stator stray inductance per phase | |
Inertia | Jr | Rotor's moment of inertia | |
Boolean | useSupport | false | Enable / disable (=fixed stator) support |
Inertia | Js | Jr | Stator's moment of inertia |
Boolean | useThermalPort | false | Enable / disable (=fixed temperatures) thermal port |
FrictionParameters | frictionParameters | Friction loss parameter record | |
CoreParameters | statorCoreParameters | Stator core loss parameter record; all parameters refer to stator side | |
StrayLoadParameters | strayLoadParameters | Stray load loss parameter record | |
Temperature | TrOperational | Operational temperature of (optional) damper cage | |
Inductance | Lmd | Stator main field inductance per phase in d-axis | |
Inductance | Lmq | Stator main field inductance per phase in q-axis | |
Boolean | useDamperCage | Enable / disable damper cage | |
Inductance | Lrsigmad | Damper stray inductance in d-axis | |
Inductance | Lrsigmaq | Lrsigmad | Damper stray inductance in q-axis |
Resistance | Rrd | Damper resistance in d-axis at TRef | |
Resistance | Rrq | Rrd | Damper resistance in q-axis at TRef |
Temperature | TrRef | Reference temperature of damper resistances in d- and q-axis | |
LinearTemperatureCoefficient20 | alpha20r | Temperature coefficient of damper resistances in d- and q-axis |
| Type | Name | Description |
|---|---|---|
Flange_a | flange | Shaft |
Flange_a | support | Support at which the reaction torque is acting |
PositivePlug | plug_sp | Positive stator plug |
NegativePlug | plug_sn | Negative stator plug |
ThermalPortSMR | thermalPort | |
output RealOutput | ir[2] | Damper cage currents |
output RealOutput | idq_dr[2] | Damper space phasor current / rotor fixed frame |